[Locally Stored Profiles] Improved Save/Share/Compare panels (Incl. local saving UI)

[violasong]

• Share: Simpler privacy notice. Copy-to-clipboard button.
• Save: Include "saved locally" confirmation with auto-named profile. Possibly also include pencil button for renaming profile (#448)
• Compare (#470): Include list of locally saved profiles

┆Issue is synchronized with this Jira Task

[digitarald]

Blocked by #11

[gregtatum]

We should re-evaluate how we build saved panels after #784 lands, as we'll have a file viewer for free.